You may well lose the pictures. What's happened is the power failure has corrupted the memory stick.
Go to one of the download sites like MajorGeeks or FileHippo and look for a program which can rescue digital pictures from memory.
Alternatively if your computer has a slot for Sony memory sticks (or buy a USB memory card reader) insert the problem stick and try the normal Windows disk tools by selecting the stick in My Computer and right clicking on it and selecting Properties, Tools, Disk Check.
If that doesn't help you may have to format the stick and lose the pictures. In Windows when doing so do not select NTFS as the way of formatting.
If after formatting the card appears to work as a disk in Windows, put it back in the camera and format it again.